How does the placement of a lens behind a slit affect the diffraction pattern?

[imagemania]

Homework Statement

How does adding a lens behind a slit alter the diffraction pattern given you know it's focal length?

Homework Equations

I know currently that i'd look at equations such as:
$$y_{n} = \frac{nD\lambda}{d}$$
Destructive and so fourth

But what about the lens, does that come into the equations anywhere?

Thanks!

 

[PeterO]

Homework Statement

How does adding a lens behind a slit alter the diffraction pattern given you know it's focal length?

Homework Equations

I know currently that i'd look at equations such as:
$$y_{n} = \frac{nD\lambda}{d}$$
Destructive and so fourth

But what about the lens, does that come into the equations anywhere?

Thanks!

The way I see it, after the light passes througgh the slit, we have it spreading out - to ultimately show a pattern spread on the wall.

If we use a diverging lens, the pattern will be spread out even more.

With a converging lens, it depends where we place the lens.

If the slit is at the focal point, then the spreading light will then travel parallel, so the first minimum would be closer to the centre.
If the lens is placed more than one focal length away, the light will be coming back together.

If the lens is placed less than a focal length from the slits, the spreading will be reduced.